Hermite Polynomials for Solving Volterra-Fredholm Integro-Differential Equations

Abstract

      In this paper, Hermite polynomials (HPs) are introduced to solve the 2^nd kind Volterra-Fredholm integro-differential equations (VFIDEs) of the first and second order. This technique is based on replacing the unknown function “infinite series” by truncated series of that is well know by Hermite expansion of functions. The presented method converts the equation into matrix form or  a system of algebraic equations with Hermite coefficients which they must be determined. The existence and uniqueness of the solution are proved.The convergence analysis of the method are studied.Some examples for the first, and second orders of 2^nd kind VFIDEs are given to demonstrate the effectiveness and the precision of the proposed method.